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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:2, 317-326
Volume 26, No 2, 2019, P. 129-144
UDC 519.1
A. A. Sapozhenko and V. G. Sargsyan
Asymptotics for the logarithm of the number of $(k, l)$-solution-free collections in an interval of naturals
Abstract:
A collection $(A_1, \ldots , A_{k+l})$ of subsets of an interval $[1, n]$ of naturals is called $(k, l)$-solution-free if there is no set $(a_1, \ldots , a_{k+l}) \in A_1 \times \cdots \times A_{k+l}$ that is a solution to the equation $x_1 + \cdots + x_k = x_{k+1} + \cdots + x_{k+l}$. We obtain the asymptotics for the logarithm of the number of sets $(k, l)$-free of solutions in an interval $[1, n]$ of naturals.
Bibliogr. 17.
Keywords: set, group, coset, characteristic function, progression.
DOI: 10.33048/daio.2019.26.610
Alexandr A. Sapozhenko 1
Vahe G. Sargsyan 1
1. Lomonosov Moscow State University,
1 Leninskie Gory, 119991 Moscow, Russia
e-mail: sapozhenko@mail.ru, vahe_sargsyan@ymail.com
Received February 20, 2018
Revised December 10, 2018
Accepted February 27, 2019
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